The criminals also claim to have carried out a distributed denial of service attack on the company, a new tactic that has been adopted recently by some gangs to put pressure on victims to yield to a ransom demand.
iTWire contacted the company on Monday, but has not heard back. Another request for comment was sent on Friday morning.
JSW Steel is an Indian-owned group which has a market value of US$12 billion (A$16.9 billion), as of 31 March, according to the website of the group's US operations. It employs more than 40,000 people globally.
There are two operations in the US, in Ohio and Texas, and it is the latter which appears to have been attacked.
The Indian operations are headquartered in Mumbai.
SunCrypt is a relatively new player in the ransomware space, having started operations in October last year.
Earlier this year, the ransomware was used to attack the Irish company Glen Dimplex Home Appliances.